Burnett won the business after a pitch against its fellow McDonald's roster networks TBWA Worldwide and DDB Worldwide.
The network is expected to develop one central creative idea, which will be articulated by its local agencies in key markets. The pitch was run by McDonald's Chicago office.
The Big Mac work will fit into the overarching creative theme of McDonald's "I'm lovin' it" campaign, which was developed by the Munich-based Heye & Partner, part of the DDB network.
McDonald's unveiled the "I'm lovin' it" positioning - its first global campaign in the chain's 50-year history - in June against a backdrop of falling sales, changes in consumer attitudes to fast food and competition both from established rivals such as Burger King and from coffee shop chains and health-food restaurants.
The positioning was chosen after a creative "competition of ideas" open to McDonald's roster agencies worldwide.
Last month, McDonald's consolidated its $1.2 billion global planning and buying into Omnicom's OMD.
The global media brief was previously shared by OMD, Publicis' Starcom network and the Grey-owned MediaCom. McDonald's awarded the account to OMD without a pitch.
The £38 million UK account moves out of Starcom Motive. OMD also handles McDonald's in France, Italy, Switzerland and the Nordic regions.
Leo Burnett and McDonalds were not available for comment as Campaign went to press.